Grade:6 Unit:2 Week:4 Dates: 10/22-10/26 Content: Positive and Negative Numbers, Points on a Coordinate Plane
Theme Essential Question:
Can students apply and extend previous understandings of multiplication/division and the number system to divide a fraction by a fraction, find common factors/ multiples and extend to the rational number system?
Essential Questions:
Can students use positive and negative numbers to represent real-world quantities?
Can students plot rational numbers on a number line?
Can students identify the relationship between points on a coordinate plane?
Standards Apply and extend previous understandings of numbers to the system of rational numbers.
6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
Objectives
Students will use positive and negative numbers to represent real-world quantities.
Students will plot rational numbers on a number line, and use a number line to identify opposites.
Students will identify the relationship between points on a coordinate plane.
Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team
Integers, positive and negative numbers, are a perfect place to use Mathematical Practice #4-Model with mathematics. This week focuses on the introduction to and the graphing of integers and rational numbers. This is not the time to work on any operations with them.
(Taken from Ohio Department of Education Teaching)
The purpose of this cluster is to begin study of the existence of negative numbers, their relationship to positive numbers. Starting with examples of having/owing and above/below zero sets the stage for understanding that there is a mathematical way to describe opposites. Students should already be familiar with the counting numbers (positive whole numbers and zero), as well as with fractions and decimals (also positive). They are now ready to understand that all numbers have an opposite. These special numbers can be shown on vertical or horizontal number lines, which then can be used to solve simple problems. Demonstration of understanding of positives and negatives involves translating among words, numbers and models: given the words “7 degrees below zero,” showing it on a thermometer and writing -7; given -4 on a number line, writing a real-life example and mathematically -4.
Background Information Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials.
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary
Math
Positive
Negative
Number line
Opposites
Coordinate plane
Suggested Activities
On Core Mathematics
Understanding Positive and Negative Numbers Lesson 37 p73-74
Rational Numbers and the Number Line Lesson 38 p75-76
Ordered Pair Relationship Lesson 39 p77-78
Mastering the Common Core ABC
Chapter 3 p26-30
Chapter 4 p36-41
Chapter 5 p54-59
Teaching the Common Core Math Standards with Hands-On Activities Grades 6-8
Compare and order integers using moveable points on a number line. Also explore the opposites of numbers on the number line.
Real Number Line - Activity A
Use a number line to compare numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers.
Real Number Line - Activity A
Identify the coordinates of points in the coordinate plane. Drag the points in the plane and investigate how the coordinates change in response.
JBHM
6th GP2, Unit 2 SBL-6: Coordinate Geometry
7th GP1, Unit 2 SBL-1: Comparing and Ordering Integers
Glencoe
6th 8-1, 8-6
7th 3-3, p117,
Highly Recommended: The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Tasks that illustrate content standard 6.NS.5, 6.NS.6a,b:
Grade:6 Unit:2 Week:4 Dates: 10/22-10/26
Content: Positive and Negative Numbers, Points on a Coordinate Plane
Theme Essential Question:
Can students apply and extend previous understandings of multiplication/division and the number system to divide a fraction by a fraction, find common factors/ multiples and extend to the rational number system?
Essential Questions:
Standards
Apply and extend previous understandings of numbers to the system of rational numbers.
Objectives
Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team
Integers, positive and negative numbers, are a perfect place to use Mathematical Practice #4-Model with mathematics. This week focuses on the introduction to and the graphing of integers and rational numbers. This is not the time to work on any operations with them.
(Taken from Ohio Department of Education Teaching)
The purpose of this cluster is to begin study of the existence of negative numbers, their relationship to positive numbers. Starting with examples of having/owing and above/below zero sets the stage for understanding that there is a mathematical way to describe opposites. Students should already be familiar with the counting numbers (positive whole numbers and zero), as well as with fractions and decimals (also positive). They are now ready to understand that all numbers have an opposite. These special numbers can be shown on vertical or horizontal number lines, which then can be used to solve simple problems. Demonstration of understanding of positives and negatives involves translating among words, numbers and models: given the words “7 degrees below zero,” showing it on a thermometer and writing -7; given -4 on a number line, writing a real-life example and mathematically -4.
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials.
Assessment
Product
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary
Negative
Number line
Opposites
Coordinate plane
Suggested Activities
On Core Mathematics
- Understanding Positive and Negative Numbers Lesson 37 p73-74
- Rational Numbers and the Number Line Lesson 38 p75-76
- Ordered Pair Relationship Lesson 39 p77-78
Mastering the Common Core ABC- Chapter 3 p26-30
- Chapter 4 p36-41
- Chapter 5 p54-59
Teaching the Common Core Math Standards with Hands-On Activities Grades 6-8- Finding the Opposite p19 (http://www.dltk-kids.com/world/japan/mfortune-teller.htm )
Gizmos- Comparing and Ordering Integers
- Compare and order integers using moveable points on a number line. Also explore the opposites of numbers on the number line.
- Real Number Line - Activity A
- Use a number line to compare numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers.
- Real Number Line - Activity A
- Identify the coordinates of points in the coordinate plane. Drag the points in the plane and investigate how the coordinates change in response.
JBHM- 6th GP2, Unit 2 SBL-6: Coordinate Geometry
- 7th GP1, Unit 2 SBL-1: Comparing and Ordering Integers
Glencoe- 6th 8-1, 8-6
- 7th 3-3, p117,
Highly Recommended: The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.Tasks that illustrate content standard 6.NS.5, 6.NS.6a,b:
- It’s Warmer in Miami http://illustrativemathematics.org/illustrations/277
- Mile High http://illustrativemathematics.org/illustrations/278
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